The h-vector of a Gorenstein codimension three domain
release_q2sztx6kivghfmsrfq4axjburi
by
E. De Negri, G. Valla
1995 Volume 138, p113-140
Abstract
Let <jats:italic>k</jats:italic> be an infinite field and <jats:italic>A</jats:italic> a <jats:italic>standard G-algebra</jats:italic>. This means that there exists a positive integer <jats:italic>n</jats:italic> such that <jats:italic>A = R/I</jats:italic> where <jats:italic>R</jats:italic> is the polynomial ring <jats:italic>R := k[X<jats:sub>v</jats:sub>
</jats:italic> …, <jats:italic>X<jats:sub>n</jats:sub>]</jats:italic> and <jats:italic>I</jats:italic> is an homogeneous ideal of <jats:italic>R</jats:italic>. Thus the additive group of <jats:italic>A</jats:italic> has a direct sum decomposition <jats:italic>A</jats:italic> = ⊕ <jats:italic>A<jats:sub>t</jats:sub>
</jats:italic> where <jats:italic>A<jats:sub>i</jats:sub>A<jats:sub>j</jats:sub>
</jats:italic> ⊆ <jats:italic>A<jats:sub>i+j</jats:sub>
</jats:italic>. Hence, for every <jats:italic>t</jats:italic> ≥ 0, <jats:italic>A<jats:sub>t</jats:sub>
</jats:italic> is a finite-dimensional vector space over <jats:italic>k</jats:italic>. The <jats:italic>Hilbert Function</jats:italic> of <jats:italic>A</jats:italic> is defined by
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:href="S0027763000005201_inline1" xlink:type="simple" />
In application/xml+jats
format
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